By the 1830's Adam Sedgwick and Roderick Murchison established a correlation between the various types of fossils and the rock formations in the British Isles.
Then the paleontologists use the geologists' dates as evidence for the age of the fossils! The relative order of the strata was first determined by the principles of stratification. Beagle, a very strong Bible believer, made it a point to have a copy of Lyell's book for the ship's library.
(The principle of superposition was recognized as early as 1669 by Steno.) Reverend Benjamin Richardson and Reverend Joseph Townsend were a couple of early geologists involved in this work. Obviously, even Lyell was not pushing evolution at the time.
Evolution, working in tandem with geologic ages, can explain why we have index fossils, but evolution is needed to make the index fossils useful for dating strata.
While we're on this subject, you might wish to know the odds of arranging the Precambrian era, the seven geologic periods of the Paleozoic (Cambrian, Ordovician, Silurian, Devonian, Mississippian, Pennsylvanian, Permian), the three periods of the Mesozoic (Triassic, Jurassic, Cretaceous), and the two periods of the Cenozoic (Paleogene, Neogene or Tertiary, Quaternary) in their proper order by pure chance.
What does the Jurassic strata have that the Tertiary strata do not? Neutrinos penetrate the earth so easily that they would affect all strata more or less equally, to the extent that they affect anything at all.
If rock type mattered then we would expect a zircon crystal's lead content to vary dramatically within the Cambrian or Cretaceous strata according to their local rock types. Cosmic rays, on the other hand, don't penetrate that far into the earth to begin with, so we can rule them out.
Once the worth of index fossils had been established on the basis of stratification studies, they could logically be used to extend the correlation of rock formations to other continents.
At this point in time they were simply a useful tool for correlating rock formations.
Any kind of object clearly restricted to a specific point in the geologic column would do just fine.